Application of a Mathematical Programming Model to Solve the Confidence Interval of Process Capability Index S_(pk)

This study developed a mathematical programming model to determine confidence intervals of S_(pk) by converting index S_(pk) into a function of μ_y = (μ - T ) and σ_y =σ/d, constructing the feasible region of joint confidence interval with μ_y and σ_y, and then regarding S_(pk)(μ_y, σ_y) as an objective function, to overcome the shortage of point-estimate and interval-estimate calculations of the past process capability index. Then, Monte Carlo simulation was used to analyze the coverage rate in order to validate the accuracy of the proposed method. Our results demonstrate the efficacy of the proposed evaluation model using quartz crystal oscillators, a passive component commonly used in communication devices. The proposed method eliminates the complex complexity of statistical methods, and the results are optimal values largely robust to errors. The proposed model can also be applied to other complex process evaluation indices, thereby presenting manufacturers with an efficient and convenient method for the assessment of process capability.